TWI899116B - Enhanced wind turbine wake mixing - Google Patents

Abstract

Method of controlling a wind turbine comprising a rotor comprising at least a first blade, the method comprising the step of varying an induction factor of the first blade over time by dynamically changing a pitch angle of the first blade over time between a first pitch angle and a second pitch angle while the first blade is rotating, wherein the first pitch angle is different from the second pitch angle, and wherein the dynamic change of the pitch angle over time is controlled such that the respective rotational position of the first blade at which the first blade is at the first pitch angle and the respective rotational positions of the first blade at which the first blade is at the second pitch angle are displaced in time and the varying induction factor of the blade occur at different angular positions in the rotor plane over time, such that a location and/or direction of a wake formed downstream of the wind turbine is dynamically changing with respect to the rotor of the wind turbine.

Description

Enhanced wind turbine wake mixing

The present invention relates to a method for controlling a wind turbine, a wind turbine controller configured for the method of controlling a wind turbine, and a wind turbine comprising a wind turbine controller configured for the method of controlling a wind turbine and an array of wind turbines, wherein at least a first wind turbine comprises a wind turbine controller.

To meet the 1.5°C climate stabilization target outlined in the Paris Agreement, fossil fuel electricity generation will need to decline significantly in the coming years. To replace this electricity generation capacity, a significant increase in renewable energy sources, such as solar and wind power, will be needed.

The most efficient way to develop wind energy on a large scale is by placing individual wind turbines on land or offshore in so-called wind farms. These wind farms consist of multiple wind turbines, typically of the same type, dispersed throughout a particular area and typically sharing a common foundation structure. This reduces the overall capital operating costs of the turbines and allows for efficient maintenance of the wind farm, while limiting the use of land and/or sea areas.

However, as a wind turbine extracts energy from the wind, a wake is generated downstream of the turbine. In the wake of the wind turbine, the (average) wind speed decreases and the (average) turbulence increases. This adversely affects turbines located further downstream because the reduced wind speed results in lower energy production and the increased turbulence increases the fatigue loads experienced by the downstream turbines.

As the flow continues further downstream, the wake disperses and, consequently, mixes with the surrounding freestream wind, causing the wake to return to freestream conditions over time (and, therefore, with increasing distance). Due to the fact that wind turbine configuration is a trade-off between available area, installed power, and infrastructure costs, spacing wind turbines at such distances that the wake effect is minimized is economically unattractive.

To optimize power output at the wind farm level, as opposed to at the individual wind turbine level, wind farm control research has focused on steady-state optimal control, also known as axial induction control or derating. In this approach, wind turbines located upstream in the wind farm are controlled to reduce their power production (i.e., to derate their efficiency) so that wind turbines located downwind can extract slightly more energy from the wind passing through them. The goal is to find the optimal static control parameters, regardless of the wind and turbine dynamics. However, it has been found that the potential power gains of such static approaches can even result in lower overall power production compared to a steady-state “ greedy ” strategy where all turbines operate at their individual optimums.

One object of the present invention, among others, is to obtain a method for controlling a wind turbine, which method reduces the wake effect downstream of the wind turbine, wherein at least one of the above-mentioned problems is at least partially alleviated.

This and other objects are met by a method for controlling a wind turbine, the wind turbine comprising a rotor including at least a first blade, the method comprising the step of varying a coefficient of induction, particularly a radial coefficient of induction, of the first blade over time by dynamically varying the pitch angle of the first blade between a first pitch angle and a second pitch angle over time as the first blade rotates, wherein the first pitch angle is different from the second pitch angle, and wherein the dynamic variation of the pitch angle over time causes a temporal shift in the rotational position of the first blade when the blade is at the first pitch angle and the second pitch angle, such that the position and/or direction of a wake formed downstream of the wind turbine relative to the rotor of the wind turbine is dynamically varied.

In another aspect of the present invention, instead of dynamically changing the position and/or direction of the wake formed downstream of the wind turbine relative to the wind turbine rotor, it is also possible to control the dynamic change of the pitch angle over time, so that the shape of the wake formed downstream of the wind turbine (instead of the position and/or direction) changes dynamically relative to the wind turbine rotor. The changing shape may, for example, correspond to a wake having a substantially constant shape that rotates along the axis of the rotor over time, preferably at a rotational speed that is (significantly) lower than the rotational speed of the rotor.

A wind turbine includes a rotor that includes at least one blade, but typically includes multiple blades, such as two or three blades, to convert the kinetic energy of the wind into mechanical energy, which is converted into electrical energy by a generator. Specifically, the wind speed causes the blades to rotate, which in turn powers the generator. However, the rotating blades (effectively forming a rotor disk) slow down the wind and cause a wake to form behind the turbine. The wind in the wake has an average lower speed and an average higher turbulence than the wind passing around the rotor disk without passing through the blades of the turbine. In addition, the lower speed of the wind in the wake causes the wake to expand relative to the speed of the wind unaffected by the rotor, that is, the diameter of the wake expands beyond the diameter of the rotor. Generally speaking, a wake defines the volume of fluid (e.g., air) affected by a turbine's blades. Any turbine positioned downstream (downwind) within this wake can only use relatively slower wind speeds to rotate its blades, resulting in lower power output from the downwind turbine. Furthermore, due to the increased average turbulence, the downwind turbine will also experience increased fatigue loads, negatively impacting its lifespan.

By transferring kinetic energy from the wind surrounding the wake into the wake itself, the relative speed and turbulence differences between the wake and the surrounding air slowly decrease over time. This process is called turbulent mixing. Because turbulent mixing occurs naturally, the kinetic energy transferred from the wind to the wind turbine is eventually replaced. However, the distance required to transfer the kinetic energy to the wake depends on the wind speed. Therefore, the distance between adjacent first and second turbines (typically less than 10 rotor diameters, or 10D) may not be sufficient to return the kinetic energy received by the first turbine before the wind reaches the second turbine located downstream of the first turbine.

In general, the induction coefficient is determined by dividing the difference between the wind speed V∞ upstream of the rotor plane and _the wind speed Vd at the rotor plane (i.e., _the rotor disc) by the upstream wind speed V∞ _, so that:

Furthermore, each blade may have an associated individual induction coefficient. The induction coefficient of a blade can be varied by pitching the blade relative to the wind (i.e., rotating the blade about its longitudinal axis), thereby changing the angle between the blade's cross-section and the rotor plane. By varying the induction coefficient of a blade, one can locally alter the wind speed and direction leaving the rotor plane, and thereby, in effect, change the orientation of the wake itself.

By temporally shifting the rotational positions of the first blades when the blades are at a first pitch angle, and preferably a second pitch angle, the blade's inductive response (i.e., the varying inductive coefficient) occurs at different angular positions in the rotor plane over time. As a result, the position of the wake formed downstream of the wind turbine also dynamically changes relative to the wind turbine's rotor. This change in the wake's position increases turbulent mixing, reducing the distance required to transfer kinetic energy into the wake. Any turbines located downstream of the wind turbine are thereby minimally affected by the wake. In the case of multiple blades, the pitch angle of at least the first blade is preferably configured to vary independently of the other blades.

In a preferred embodiment, the method includes the step of dynamically changing the pitch angle of a first (e.g., concentrated) blade of a wind turbine by superimposing a periodic variation in pitch angle on the pitch angle of the first blade, thereby imposing yaw and tilt moments on the rotor to achieve forced wake mixing. The method thus has the advantage of achieving improved wake mixing by only applying slight changes to existing control methods for wind turbines (i.e., by superimposing periodic variations on the pitch angle).

In a preferred embodiment of the method, the step of varying the inductance of the first blade over time includes dynamically varying the pitch angle of the first blade according to a predefined periodic function. The predefined periodic function is defined such that the rotational position of the first blade at the first pitch angle and the second pitch angle are shifted in time. Periodically varying the pitch angle according to the predefined periodic function is a simple and effective way to ensure that the rotational position of the first blade at the first pitch angle and the second pitch angle are shifted in time, thereby dynamically varying the position and/or direction of the wake formed downstream of the wind turbine.

In a preferred embodiment of the method, the predefined cyclic function is defined such that the rotational position of the blade in the rotor plane shifts from rotation to rotation when the blade is at a first pitch angle. Due to the change in induction of the blade occurring at different angular positions in the rotor plane, the resulting thrust acting on the blade will also vary with the change in induction, so that the entire rotor experiences cyclical changes in the orientation of the thrust without significantly altering the amplitude of the force itself. As a result, only relatively small changes in thrust are experienced, so that these thrust forces do not significantly increase the fatigue loads induced on the turbine. Specifically, if the displacement between rotations is relatively slow, for example, less than 180° per rotation, preferably less than 90° per rotation, and more preferably less than 45° per rotation, then the cyclical change in thrust direction is a low-frequency force variation that does not significantly increase the fatigue load of the turbine.

In a preferred embodiment, the rotor includes a second blade, and the method includes the step of varying the inductance of the second blade over time by dynamically varying the pitch angle of the second blade between a first pitch angle and a second pitch angle, wherein the time the first blade is at the first pitch angle is different from the time the second blade is at the first pitch angle. Varying the pitch angle of the first blade may cause an imbalance in the rotor. By also dynamically varying the pitch angle of the second blade as described herein, the imbalance can be at least partially compensated.

In a preferred embodiment, the rotor includes a second blade, preferably configured such that its pitch angle can be varied separately from, or independently of, the pitch angle of the first blade, and the method preferably includes the step of varying the inductance of the second blade over time by dynamically varying the pitch angle of the second blade according to the predefined periodic function, wherein the dynamic variation of the pitch angle of the second blade is phase-shifted relative to the dynamic variation of the pitch angle of the first blade. By varying the inductance of the second blade also according to the predefined periodic function, but with a phase shift relative to the first blade, the pitch angles of the first and second blades (and therefore their inductances) are not simultaneously at their maximum or minimum values. If the induction coefficients were to be at their maximum or minimum values simultaneously, the turbine would effectively be depowered, with its power production reduced as the rotor induction coefficient changes completely, rather than producing localized changes that have only a minor effect on the overall rotor induction coefficient and therefore the turbine's power output.

It is then preferred that the phase offset is substantially equal to the angle between the first blade and the second blade in the rotor plane. For example, for a two-bladed turbine, the angle is approximately 180°. By also having a phase offset of approximately 180°, the minimum inductance of the first blade is compensated by the maximum inductance of the second blade, thereby minimizing the variation in the total inductance of the rotor. For example, for a three-bladed turbine, the angle is approximately 120°. Also by having a phase offset of approximately 120°, the minimum inductance of the first blade is substantially compensated by the other two blades.

According to a preferred embodiment of the method, the dynamic variation of the pitch angle over time is obtained by performing a reverse multiblade coordination (MBC) transformation on a time-varying yaw function defined in a non-rotating reference frame, or a time-varying pitch function defined in a non-rotating reference frame, or a combination of these time-varying yaw and pitch functions. Multiblade coordination (MBC) is typically used to transform blade moments from a local blade coordinate system to a non-rotating or ground-fixed inertial coordinate system to determine loads on, for example, a turbine tower. By defining time-varying yaw and/or pitch signals that can manipulate the wake horizontally and/or vertically, respectively, in a non-rotating coordinate system and performing an inverse MBC transformation, the signals are transformed into a local blade coordinate system, thereby obtaining a dynamic change in the pitch angle of at least the first blade.

Preferably, the time-varying yaw function is a periodic yaw function and/or the time-varying tilt function is a periodic tilt function, and a predetermined periodic function is obtained by performing the inverse multi-blade coordination (MBC) transformation, such that dynamically varying the pitch angle over time dynamically varies the pitch angle according to the predetermined periodic function. This allows for relatively simple functions to achieve the desired effects described above. Preferably, the periodic tilt function and/or the periodic yaw function are sinusoidal functions having a predetermined frequency. The inverse transformation results in a periodic pitch function for the individual blades, which is also a sinusoidal function, or a superposition of sinusoidal functions, resulting in a smooth pitch signal. Due to the size and weight of the individual blades, especially in utility-class wind turbines, a smooth pitch signal is preferred because it avoids sudden, shock-like excitations through the pitch mechanism, which could induce undesirable dynamic forces in various wind turbine structures and introduce additional loads on the turbine and its components.

In a preferred embodiment of the method, the predefined periodic function comprises a first sine function having a first frequency, wherein the first frequency is different from the rotor's rotational frequency or a multiple thereof. Alternatively, the predefined periodic function comprises a superposition of the first sine function and a second sine function having a second frequency, wherein the first frequency is different from the second frequency. As explained above, the sine function or superposition of sine functions produces a smooth periodic pitch angle change.

Preferably, the value of the first frequency or the value of the second frequency is substantially equal to the rotational frequency of the rotor plus or minus a predetermined frequency, which is a non-zero frequency less than the rotational frequency. This allows the dynamic variation of the pitch angle of at least the first blade according to the predetermined periodic function to vary relatively slowly compared to the rotational frequency of the turbine. Consequently, these low-frequency signals generate slow and smooth periodic pitch angle variations that are not expected to significantly increase the load on the turbine, while simultaneously achieving relatively slow variations in the position and direction of the wake, which results in increased wake mixing. Since the predetermined frequency is a non-zero frequency that is less than the rotation frequency, the effect of improved wake mixing is achieved as described above, while at the same time the pitching action of the blades is only slightly increased. This results in limited additional loads on the pitch system, and in particular on the pitch bearing, which is often the most fatigue-determining component of the pitch system, compared to existing individual pitch control methods, such as those used for load reduction.

The predetermined frequency is preferably determined based on at least the rotor diameter, the rotor rotational speed, and/or the incoming wind speed determined upstream of the wind turbine. This allows the predetermined periodic function to be customized for different operating conditions or turbine sizes, thereby achieving enhanced wake mixing for these different operating conditions and turbine sizes. Alternatively or additionally, the predetermined frequency is preferably determined based on at least the Struchholz number, wherein the Struchholz number is preferably between 0.05 and 1.0, more preferably between 0.15 and 0.55, and even more preferably between 0.2 and 0.3, and most preferably approximately 0.25.

The predetermined frequency of the periodic tilt and/or deflection function can be determined using a dimensionless number called the Strouhal number:

It defines the relationship between the inflow wind speed U∞ , _the turbine rotor diameter D , and a predetermined frequency f . Based on computer simulations using a simulation program (Simulator for Wind Farm Applications (SOWFA)) for different frequencies under laminar flow conditions, it is estimated that the optimal Strychnitz number is preferably between 0.05 and 1.0, more preferably between 0.15 and 0.55, and even more preferably between 0.2 and 0.3, with an optimal value of approximately 0.25. It was found that application of any specific instance with a predetermined frequency determined by this Strychnitz number resulted in excellent wake mixing.

In a preferred embodiment of the method, the difference between the first pitch angle and the second pitch angle is 30° or less, more preferably 20° or less, more preferably 10° or less, and most preferably between 2° and 8°. Excessive changes in the pitch angle will result in reduced turbine efficiency, while too small a change will not result in the desired amount of wake mixing. A good compromise between these two is found within the range given above.

In a second aspect of the present invention, a wind turbine controller is provided, which is configured to control a wind turbine including a rotor, the rotor including at least a first blade, wherein the controller is configured to change the inductance of the first blade over time by dynamically changing the pitch angle of the first blade according to a predetermined periodic function, so that the pitch angle of the first blade changes between the first and second blades when the first blade rotates. The pitch angle and a second pitch angle vary periodically, wherein the first pitch angle is different from the second pitch angle, and wherein the predetermined periodic function is defined such that the rotational position of the first blade at the first pitch angle and the second pitch angle are shifted in time, such that the controller is configured to dynamically change the positioning of a wake formed downstream of the wind turbine relative to the rotor of the wind turbine. Thus, the advantages of the control method are applied to the controller.

In a third aspect of the present invention, a wind turbine is provided, comprising a rotor including at least first blades, the wind turbine further comprising a wind turbine controller configured to control the wind turbine according to any of the methods described in the specific embodiments. This provides a wind turbine capable of improving mixing in a wake formed downstream of the turbine.

In another aspect, an array of at least two wind turbines is provided, wherein, for a given wind direction, the second wind turbine is arranged at least partially downstream in the wake of the first wind turbine, wherein the first and second wind turbines include a rotor comprising at least first blades, and wherein at least the first wind turbine includes a wind turbine controller configured for controlling a wind turbine according to the method of any of the given embodiments. This results in an array of turbines, such as in a wind power plant, wherein at least one turbine is configured to improve mixing in the wake formed downstream of the turbine, thereby further increasing the power production of the array of wind turbines (i.e., the wind power plant).

1: Wind turbine

2: Tower

3: Base

4: Aircraft cabin

5: Rotor

6: Transmission system

7: Deflection mechanism

8: Pitch mechanism

9: wake

51:Leaf

52: Leaves

53:Leaf

54: Hub/Thrust

55: Blade root section/thrust

61: Generator

62: Gearbox

63: High-speed shafts

64: Low-speed shaft

71: Deflection Motor

72: Gear rim

81: Pitch drive

82: Pitch drive

91: wake

92: Spiral wake

93: Initial section

101: First Wind Turbine

102: Second wind turbine

103: Dashed Line

104: Dashed Line

200: Flowchart

201: Step

203: Step

204: Step

205: Step

207: Step/Yaw and Tilt Moment

2011: Periodic tilt function

2012: Periodic deflection function

2071: Tilt moment

2072: Yaw moment

d: Mutual distance

I: Vertical axis

II: Rotor axis

III: Longitudinal axis

IV: Rotor plane

W: Wind direction

θ ₁ : Pitch angle

θ ₂ : Pitch angle

θ ₃ : Pitch angle

The present invention is further illustrated by the following figures, which show preferred embodiments of the method for controlling a wind turbine according to the present invention and are not intended to limit the scope of the present invention in any way, wherein: [FIG. 1A] schematically shows a horizontal axis wind turbine comprising three bladed rotors.

[Figure 1B] Schematic illustration of a pitching blade.

[Figure 2] Schematic diagram showing the nacelle and rotor of a wind turbine, including its various components.

[Figure 3] Schematic illustration of an array of two wind turbines, with the second wind turbine deployed downstream in the wake of the first wind turbine.

[Figure 4] shows a flowchart of the different steps involved in a specific example of a method for controlling a wind turbine.

Figure 5 shows a graph representing the average wake velocity at different distances behind the turbine for control based on different Stroudhall numbers. When greedy control is applied, the velocity is normalized by dividing by the wake velocity at each location.

6A and 6B schematically illustrate the wake positioning at different times during an excitation period T of a turbine controlled using two different embodiments of the method.

FIG. 7 shows the difference between the wake generated by a turbine controlled using a greedy control method and the wake generated by a turbine controlled using a specific embodiment of the method for controlling a wind turbine according to the present invention.

FIG1A schematically illustrates the layout of a typical three-bladed horizontal-axis wind turbine 1. The wind turbine comprises a tower 2 atop a foundation 3. It should be noted that such wind turbines can be deployed both onshore (e.g., onshore) and offshore (e.g., offshore). In the latter case, foundation 3 will typically be an offshore foundation, such as a fixed structure installed in the seabed, such as a pile, tripod, jacket, or alternatively a floating foundation with a floating body secured to the seabed to hold it in place. In the case of an onshore turbine, such foundation 3 is typically a so-called gravity foundation, comprising a heavy concrete body to secure the wind turbine 1 to the ground.

A cabin 4 coupled to a rotor 5 is arranged on top of the tower 2. The rotor 5 comprises three blades 51, 52, 53, but any number of blades is possible, for example one, two or four blades may also be applied. The blades 51, 52, 53 are fixed to a hub 54. The rotation of the cabin 4 about a vertical axis I which is substantially parallel to the tower 2 or coincides with the tower and which is substantially perpendicular to the ground plane is called yaw rotation. The yaw angle can be defined depending on the wind direction, in which case a non-zero yaw angle means that there is a misalignment between the direction of the rotor axis II and the wind direction W. The rotor 5 is arranged to rotate about the rotor axis II, this rotation is often called azimuth rotation. The blades 51, 52, 53 are further configured to rotate about their respective longitudinal axes III. This rotation is referred to as pitch rotation, and the angle between the central axis V of the cross section of the blades 51, 52, 53 and the rotation plane IV of the rotor 5 is referred to as the pitch angle. FIG1B shows that the central axis V of the cross section of the first blade 51 is pitched at a pitch angle θ ₁ relative to the rotor plane IV.

Figure 2 schematically illustrates the nacelle 4 and rotor 5 of a wind turbine 1, with various components arranged within the nacelle 4. The nacelle 4 houses a drive train 6, which may include a generator 61 for generating electrical energy, and a gearbox 62 disposed between a high-speed shaft 63 and a low-speed shaft 64. The low-speed shaft 64 is connected to the rotor 5, and the high-speed shaft 63 transmits rotation from the output of the gearbox 62 to the generator 61. It should be noted that in so-called direct-drive wind turbines, the rotor is typically connected directly to the generator via a main shaft or a low-speed shaft. In these types of wind turbines, the gearbox 62 and high-speed shaft 63 are not required.

Furthermore, the cabin 4 typically also includes a yaw mechanism 7 for yawing the cabin 4 about the tower 2 (particularly about the vertical axis I). The yaw mechanism 7 may include a plurality of yaw motors 71 attached to the base of the cabin 4 and including a transmission for reducing the rotational speed toward an output drive pinion, which can engage with a gear rim 72 having teeth on its inner side, which in turn is connected to the top of the tower 2. Furthermore, a pitch mechanism 8 is (at least partially) included in the hub 54, wherein the pitch mechanism 8 is configured for pitching the blades 51, 52, 53. In the present embodiment of turbine 1, pitch mechanism 8 includes three pitch actuators 81, 82, 83 configured to drive the distal ends of blade root sections 55, 56, 57 of respective blades 51, 52, 53. Pitch actuators 81, 82, 83 are configured to individually drive pitch rotation of respective blades 51, 52, 53, such that blades 51, 52, 53 may have different pitch angles at any given time. This pitch mechanism 8 is also referred to as an individual pitch mechanism, and controlling the individual pitch mechanisms to minimize fatigue loads on the turbine is referred to as individual pitch control (IPC).

Figure 3 schematically illustrates an array of two wind turbines, where the wind direction W places second wind turbine 102 downstream in the wake of first wind turbine 101. A wake can be considered a region where the (average) wind speed decreases and turbulence increases, as indicated between dashed lines 103 and 104. The wake caused by wind turbine 101 slowly mixes with the surrounding (undisturbed) wind farm, and due to this mixing, the wake effect decreases with increasing distance from the turbine. The turbines 101, 102 are typically placed at a mutual distance d of three to ten times the rotor diameter (3D to 10D), wherein a mutual distance of ten times the rotor diameter significantly results in lower wake effects, such as reduced power output and reduced vibrations, and thereby reduces the induced fatigue loads on the various wind turbine components, compared to a mutual distance of only three times the distance. However, as already described above, wind turbines typically must be developed within limited space, so that a longer mutual distance can result in a reduction in the power output of the entire turbine and, thereby, an increase in the cost of the generated energy. Therefore, it would be beneficial to be able to increase wake mixing and reduce the length and/or strength of the wake, allowing turbines to be placed at a shorter distance while still providing higher power output while inducing fewer fatigue loads.

FIG4 shows a block diagram or flow chart 200 of steps for a specific embodiment of a control method for controlling a wind turbine. In step 201, periodic pitch and yaw functions 2011, 2012 are defined, wherein the periodic pitch and yaw functions 2011, 2012 are defined as sinusoidal functions with a common predetermined frequency f , and wherein the periodic pitch and yaw functions 2011, 2012 have a phase offset of preferably 90° or 270°. Thus, in this particular embodiment, referred to as a spiral IPC, both pitch and yaw degrees of freedom are activated, but with a phase offset of π/2 radians (90°). This causes the torque on the rotor (as seen in a non-rotating coordinate system) to rotate over time, completing one rotation every T = 1/f seconds and producing a spiral wake 92, as seen in FIG7 .

The predetermined frequency f of the periodic tilt and deflection functions 2011 and 2012 can be determined based on a dimensionless number called the Stroudsho number relative to _the inflow wind speed U∞ and the turbine rotor diameter D :

The optimal Strychow number is preferably between 0.05 and 1.0, more preferably between 0.15 and 0.55, and even more preferably between 0.2 and 0.3, with an optimal value of approximately 0.25. An estimate of this optimal value was obtained by performing a grid search in a simulator (Simulator for Wind Farm Applications (SOWFA)) for different frequencies under laminar flow conditions. The resulting average wake velocity at different distances behind the excited turbine is shown in FIG5 , which shows a graph representing the average wake velocity at different distances behind the turbine for turbines excited at different frequencies. When greedy control is applied, the velocity is normalized by dividing by the wake velocity at each location. FIG5 shows that for a number of different distances from the rotor, where the distances are given in terms of rotor diameter D (3D, 5D, and 7D), the peak value is approximately St = 0.25. Based on these results, the Stryker number can be selected for determining the excitation frequency. Furthermore, the pitch amplitude β is preferably 15° or less, more preferably 10° or less, even more preferably 5° or less, and most preferably between 2° and 4°, as excessive pitch amplitudes of (preferably) sinusoidal pitch variations lead to increased turbine loads.

An inverse multi-blade coordination (MBC) transformation step (203) is applied to obtain the periodic variation of the pitch angles θ ₁ , θ ₂ , θ ₃ of the individual blades 51 , 52 , 53 . The MBC transformation decouples or in other words projects the blade loads in a non-rotating reference frame and is a transformation used, for example, in individual pitch control methods to reduce fatigue loads in wind turbines. The n-times-per-revolution ( n P) load harmonics, which depend on the rotor speed, are transferred to the steady-state contribution, thereby simplifying the controller design. The equations implementing the transformation are summarized. The measured out-of-plane blade root bending moment M(t) RB is fed into a forward transform, thereby transforming the rotating blade torque to a non-rotating reference frame (as also shown ^, for example, in step 207):

in

where n Z ⁺ is the harmonic wave number, B Z ⁺ is the total amount of leaves, and ψ _b R is the leaf b _The azimuth angle of Z ⁺ , where ψ = 0° indicates the vertical upright position. The collective mode M0 represents the accumulated out-of-plane rotor moment, and Mt _and My represent the fixed coordinate system and azimuth-independent _tilt and yaw moments (2071, 2072), respectively. The latter two components are typically used for the purpose of reducing fatigue loads.

By applying the inverse MBC transform to the non-rotated signal (of step 201), this produces the individual pitch contributions that can be implemented in the rotational (i.e., blade) coordinate system.

in

where θ _0,n , θ _t,n and θ _y,n are the fixed coordinate set, tilt and yaw pitch signals, respectively, and ψ _o,n is the azimuth offset of each harmonic.

The possibility of individually driving the pitch of the rotor blades, for example using pitch actuators 81, 82, 83, is now used to increase the wake recovery effect, or in other words, to increase wake mixing. By individually pitching the blades, the thrust of the turbine and subsequently the power production can be controlled to a value close to the greedy optimum (step 205).

As an example, the proposed control strategy is evaluated in the Simulator for Wind Farm Applications (SOWFA), a high-fidelity simulation environment developed by the National Renewable Energy Laboratory (NREL). SOWFA is a large vortex solver for the dynamics of fluids in turbulent atmospheres and their interaction with one or more wind turbines, accounting for Coriolis and buoyancy effects. The turbine is modeled as an actuating disk or actuating wire. In this work, SOWFA is adapted to allow specification of different pitch setpoints for each individual blade. The simulation in this work features a neutral atmospheric boundary layer (ABL), where the inflow is generated via a so-called drivetrain simulation. Several properties of the simulation setup are listed below.

Numerical simulation solution in SOWFA:

Turbine: NREL 5MW reference turbine

Rotor diameter: 126.4m

Domain size: 3km×3km×1km

Unit size (external area): 10m×10m×10m

Unit size (near the rotor): 1.25m × 1.25m × 1.25m

ABL stability: Neutral

Inflow wind speed: 8.0m/s

Inflow turbulence intensity: 5.9%

As a baseline for the comparison method according to the present invention, a so-called greedy control strategy is used. This approach means that interactions between wind turbines are ignored, and therefore all turbines are operated at their individual optimum. This means that the rotors are yawed perpendicular to the wind, and for wind speeds below a rated value, the pitch angle and generator torque are controlled to achieve the optimal power extraction from the wind. This situation serves as a good baseline because it is still the strategy commonly implemented in wind power plants. With this strategy, power production from the upstream turbine is optimized, but the wake losses are relatively high, resulting in lower efficiency for the downstream machines.

In a control method according to an embodiment of the present invention, pitching the blades individually according to periodic variations in pitch angles θ ₁ , θ ₂ , θ ₃ is used to stimulate wake mixing by individually changing the blade inductance and thereby the yaw angle of attack of the turbine. As explained above, the control method enables the imposition of yaw and pitch moments on the rotor by applying an MBC transformation, as seen in step 207. These yaw and pitch moments 207 can then result in forced wake mixing with relatively small changes in electrical power and wake velocity. This is achieved by superimposing the periodic variation of the pitch angles θ ₁ , θ ₂ , θ ₃ on the common blade pitch angle of the wind turbine (step 204 ).

These projected loading signals are first transformed into a rotated coordinate system using the MBC transformation explained above to obtain the implemented pitch angle. For identical sinusoidal tilt and yaw signals, where the yaw signal has a 90° phase delay, this produces sinusoidal pitch signals β with different frequencies according to the common trigonometric formula:

where ψ _b is the azimuthal position of blade number b, f _h is the new spiral excitation frequency, and φ _b is the phase offset of blade b. Therefore, we can determine f _h = f + f _r , where f _r is the rotor rotation frequency. For the NREL 5MW reference turbine, the rotor speed at U _∞ = 8 m/s is equal to f _r 9.5rpm 0.158 Hz. Therefore, the pitch frequency f _h of the specific example called helical IPC will be slightly higher than the rotation frequency of the blade; where St = 0.25, f _h 0.174Hz.

For example, an alternative embodiment has been found if the periodic tilt function 2011 is set to zero (skew IPC), or alternatively, the periodic tilt function 2012 is set to zero (skew IPC). In that case, the inverse MBC (step 203) and common trigonometric formulas result in a periodic variation of the pitch angles θ ₁ , θ ₂ , θ ₃ , wherein the periodic variation then becomes the superposition of two sinusoidal signals, a first sinusoidal signal having a first frequency f _h = f + f _r and a second sinusoidal signal having a second frequency f _h = f _r - f .

For example, the effect of applying a periodic variation of the pitch angles θ ₁ , θ ₂ , θ ₃ on individual blades 51 , 52 , 53 is schematically illustrated in FIG6A and FIG6B . FIG6A shows a schematic representation of the positioning of the wake 9 at different times during one cycle T = 1/f of a specific embodiment known as tilt IPC. In the tilt IPC embodiment, the periodic deflection function 2012 is set to zero, and a sinusoidal tilt function with a predetermined frequency f is used to determine a predetermined periodic function by which the pitch angle of the individual blades is varied. As seen perpendicularly to the rotor plane IV, the positioning of the wake 9 varies dynamically between an upper position and a lower position relative to the rotor 5 during the course of a period T , where T = 1/f .

FIG6B shows the resulting change in the positioning of the wake 9 due to the spiral IPC. During a period T = 1/f , the position of the wake 9 relative to the rotor is determined at different times. As viewed perpendicular to rotor plane IV, the positioning of the wake 9 changes dynamically. At t = 0, the wake 9 loops from its upper position relative to the rotor 5, to its rightmost position at t = T/4 , to its lower position at t = T/2 , to its leftmost position at t = 3T/4 , and back to its upper position at t = T , completing a complete loop over the course of a period T , where T = 1/f . As shown in FIG7 and described below, the spiral IPC embodiment generates a spiral wake around the rotor axis, hence its name. These simulations were performed with a 90° phase shift between the (identical) tilt and yaw signals, resulting in a clockwise (CW) rotational motion of the helix around the rotor axis, as seen from an upwind direction parallel to the rotor axis. With a 270° phase shift between the tilt and yaw signals, a counterclockwise (CCW) rotational motion of the helix around the rotor axis was obtained.

To evaluate the impact of specific instances of helix, pitch, and yaw IPC on the turbine's power production and the resulting wake impairment, 1000 simulations (1000 seconds) were performed in the SOWFA solver. The results of these simulations are shown in the table below.

This table presents the results of simulations in SOWFA for clockwise and counterclockwise spiral IPC, pitch IPC, and yaw IPC examples of the control method. The clockwise (CW) and counterclockwise (CCW) spiral IPC examples were evaluated with pitch amplitudes β between 2.5° and 4°. The results are presented in terms of power production, power and thrust changes, and wake recovery. All results are presented relative to a baseline case of greedy control.

For the tested examples, the new control method resulted in a maximum power loss of only 5.3% compared to the baseline. On the other hand, the amount of energy in the wake increased by up to 26%. For all tested examples, the new control method also resulted in reduced power variability, meaning more constant power production, which benefits grid stability. Furthermore, power variability and thrust variability were reduced, demonstrating the advantages of the method not only in wind farm settings, but also for individual turbines, aiming to provide more stable power output (i.e., less variability) and reduce certain fatigue loads attributable to thrust generation (i.e., lower thrust variability).

FIG7 shows, on the left, a wind turbine 1 comprising a rotor 5 with three blades 51, 52, and 53 for a baseline greedy control scenario. Downstream of turbine 1, a wake 91 is shown, where the gray segments represent reduced wind speed relative to the surrounding air. The darker the gray, the greater the reduction. Thus, it can be seen that wake 91 shows minimal signs of mixing even at a distance of ten times the rotor diameter (10D). Also shown is thrust 54, which is mirrored relative to rotor plane IV. The orientation of thrust 54 remains essentially static over time (i.e., its direction exhibits virtually no change over time). It should be noted that the simulations used to obtain FIG. 7 have been performed based on a uniform inflow in order to clearly illustrate the resulting spiral wake.

The right-hand part of FIG. 7 shows the same turbine 1 , which is controlled using the spiral IPC embodiment of the control method to generate a (rotating) spiral wake 92 behind the turbine. Due to this spiral wake 92 , the wake mixing with the surrounding air increases, whereby the wake dissolves more quickly. At a distance of approximately 5D, the wake effect is significantly reduced. As a result, wind turbines controlled using the control method according to the present invention can be placed closer to each other than more conventionally controlled wind turbines, thereby increasing the potential power production of the wind power plant. Thrust 55 is also shown, which is mirrored relative to the rotor plane IV. Using the spiral IPC embodiment, thrust 55 actually shows a slight directional change relative to the incoming wind compared to thrust 54 . It can be seen that the direction of the thrust 55 changes during operation and actually cycles along the rotor in synchronization with the cycle of the initial segment (i.e., origin) 93 of the wake 92. This is due to the fact that the predetermined periodic function is defined such that the rotational position of the blade in the rotor plane shifts from rotation to rotation when the blade is at a first pitch angle.

The present invention is not limited to the specific examples shown, but also extends to other specific examples within the scope of the attached patent applications.

200: Flowchart

201: Step

203: Step

204: Step

205: Step

207: Step/Yaw and Tilt Moment

2011: Periodic tilt function

2012: Periodic deflection function

2071: Tilt moment

2072: Yaw moment

θ ₁ : Pitch angle

θ ₂ : Pitch angle

θ ₃ : Pitch angle

Claims (19)

A method of controlling a wind turbine, the wind turbine comprising a rotor comprising at least one first blade, the method comprising the steps of varying an induction coefficient of the first blade over time by dynamically varying a pitch angle of the first blade between a first pitch angle and a second pitch angle over time as the first blade rotates, wherein the dynamic variation of the pitch angle of the first blade over time is controlled such that when the first blade is at the first pitch angle, the first blade is in a rotor plane. The respective rotational positions of the first blades are displaced during rotation and the respective rotational positions of the first blades in the rotor plane are displaced during rotation when the first blades are at the second pitch angle, and the change in the induction coefficient of the first blades occurs at different angular positions in the rotor plane over time, so that the direction of the thrust of the entire rotor changes periodically without significantly changing the amplitude of the force itself, so that the position and/or direction of a wake formed downstream of the wind turbine changes dynamically relative to the rotor of the wind turbine. In the method for controlling a wind turbine as claimed in claim 1, the wake downstream of the wind turbine is a helical wake. A method of controlling a wind turbine as claimed in claim 1, comprising the steps of dynamically changing a pitch angle of the first blade by superimposing a periodic variation of the pitch angle of the first blade to impose a yaw and/or pitch moment on the rotor for obtaining forced wake mixing. A method of controlling a wind turbine as claimed in claim 3, wherein the step of causing the induction coefficient of the first blade to vary over time comprises dynamically changing the pitch angle of the first blade according to a predetermined periodic function, and wherein the predetermined periodic function is defined such that the respective rotational positions of the first blade are displaced in time when the first blade is at the first pitch angle and the second pitch angle. A method of controlling a wind turbine as claimed in claim 1 or 2, wherein the rotor includes a second blade, the method comprising the steps of varying an inductance of the second blade over time by dynamically varying a pitch angle of the second blade between a first pitch angle and a second pitch angle, wherein a time that the first blade is at the first pitch angle is different from a time that the second blade is at the first pitch angle. A method for controlling a wind turbine as claimed in claim 4, wherein the rotor includes a second blade, the method comprising the steps of varying an inductance of the second blade over time by dynamically varying a pitch angle of the second blade according to the predetermined periodic function, wherein the dynamic variation of the pitch angle of the second blade is phase-offset from the dynamic variation of the pitch angle of the first blade. A method of controlling a wind turbine as claimed in claim 6, wherein the phase offset is substantially equal to an angle between the first blade and the second blade in the rotor plane. A method of controlling a wind turbine as claimed in claim 4, wherein the dynamic change of the pitch angle over time is obtained by performing an inverse multi-blade coordination (MBC) transformation on a time-varying yaw function defined in a non-rotating reference coordinate system, or on a time-varying pitch function defined in a non-rotating reference coordinate system, or on a combination of the time-varying yaw function and the time-varying pitch function. A method for controlling a wind turbine as claimed in claim 8, wherein the time-varying yaw function is a periodic yaw function and/or the time-varying pitch function is a periodic pitch function, and wherein a predetermined periodic function is obtained by performing the inverse multi-blade coordination (MBC) transformation, so that dynamically changing the pitch angle over time dynamically changes the pitch angle according to the predetermined periodic function. A method for controlling a wind turbine as claimed in claim 9, wherein the periodic tilt function and/or the periodic yaw function is a sinusoidal function having a predetermined frequency. A method of controlling a wind turbine as claimed in claim 4, wherein the predefined periodic function comprises a first sinusoidal function having a first frequency, wherein the first frequency is different from the rotation frequency of the rotor or a multiple thereof. A method of controlling a wind turbine as claimed in claim 11, wherein the predefined periodic function comprises a superposition of the first sinusoidal function and a second sinusoidal function having a second frequency, wherein the first frequency is different from the second frequency. A method of controlling a wind turbine as claimed in claim 12, wherein the value of the first frequency or the value of the second frequency is substantially equal to the rotational frequency of the rotor plus or minus a predetermined frequency, the predetermined frequency being a non-zero frequency less than the rotational frequency. A method for controlling a wind turbine as claimed in claim 10, wherein the predetermined frequency is determined based on at least a diameter of the rotor, a rotational speed of the rotor and/or an incoming wind speed determined upstream of the wind turbine. The method for controlling a wind turbine as claimed in claim 10, wherein the predetermined frequency is determined based on at least a Stryker number. A method for controlling a wind turbine as claimed in claim 1, wherein the difference between the first pitch angle and the second pitch angle is 30°. A wind turbine controller is configured to control a wind turbine, wherein the wind turbine controller controls the wind turbine according to the method for controlling a wind turbine as claimed in any one of claims 1 to 16. A wind turbine comprising: a rotor comprising at least one first blade; and a wind turbine controller as claimed in claim 17. An array of at least two wind turbines, wherein, for a given wind direction, a second wind turbine is disposed at least partially downstream in a wake of a first wind turbine; wherein at least the first wind turbine is as described in claim 18; and the second wind turbine includes a rotor including at least one first blade.